On Generalized Picard Integral Operators

Abstract

In the paper, we constructed a class of linear positive operators generalizing Picard integral operators which preserve the functions \(e^{\mu x}\) and \(e^{2\mu x},\)\(\mu >0.\) We show that these operators are approximation processes in a suitable weighted spaces. The uniform weighted approximation order of constructed operators is given via exponential weighted modulus of smoothness. We also obtain their shape preserving properties considering exponential convexity.